Definition:Airy Function

Definition

An Airy function is a special function.

An Airy function is a solution to Airy's equation:

$\dfrac {\d^2 y} {\d x^2} = x y$

Airy Function of the First Kind

An Airy function of the first kind is an Airy function which is of the form:

$\ds \map {\Ai} x = \dfrac 1 \pi \int_0^\infty \map \cos {\dfrac {t^3} 3 + x t} \rd t$

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Also see

• Results about Airy functions can be found here.

Source of Name

This entry was named for George Biddell Airy.

Historical Note

The Airy functions were first investigated to address the question of the appearance of a star in a telescope.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Airy functions